Finiteness properties and profinite completions

Alexander Lubotzky

doi:10.1112/blms/bdt070

Finiteness properties and profinite completions

Alexander Lubotzky^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ₁ and Γ₂ with isomorphic profinite completions, such that Γ₁ is strictly of type F_k and Γ₂ of type F_ℓ.

Original language	English
Pages (from-to)	103-110
Number of pages	8
Journal	Bulletin of the London Mathematical Society
Volume	46
Issue number	1
DOIs	https://doi.org/10.1112/blms/bdt070
State	Published - Feb 2014

Access to Document

10.1112/blms/bdt070

Cite this

@article{621a2c2ad8754be7a571c69b1a00067e,

title = "Finiteness properties and profinite completions",

abstract = "In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ1 and Γ2 with isomorphic profinite completions, such that Γ1 is strictly of type Fk and Γ2 of type Fℓ.",

author = "Alexander Lubotzky",

year = "2014",

month = feb,

doi = "10.1112/blms/bdt070",

language = "אנגלית",

volume = "46",

pages = "103--110",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Finiteness properties and profinite completions

AU - Lubotzky, Alexander

PY - 2014/2

Y1 - 2014/2

N2 - In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ1 and Γ2 with isomorphic profinite completions, such that Γ1 is strictly of type Fk and Γ2 of type Fℓ.

AB - In this note, we show that various (geometric/homological) finiteness properties are not profinite properties. For example, for all positive integers k and ℓ, there exist two finitely generated residually finite groups Γ1 and Γ2 with isomorphic profinite completions, such that Γ1 is strictly of type Fk and Γ2 of type Fℓ.

UR - http://www.scopus.com/inward/record.url?scp=84892731389&partnerID=8YFLogxK

U2 - 10.1112/blms/bdt070

DO - 10.1112/blms/bdt070

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84892731389

SN - 0024-6093

VL - 46

SP - 103

EP - 110

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

Finiteness properties and profinite completions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this